Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x+8y &= 4 \\ 4x-8y &= 6\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $4x = 8y+6$ Divide both sides by $4$ to isolate $x$ $x = {2y + \dfrac{3}{2}}$ Substitute this expression for $x$ in the first equation. $6({2y + \dfrac{3}{2}}) + 8y = 4$ $12y + 9 + 8y = 4$ Simplify by combining terms, then solve for $y$ $20y + 9 = 4$ $20y = -5$ $y = -\dfrac{1}{4}$ Substitute $-\dfrac{1}{4}$ for $y$ in the top equation. $6x+8( -\dfrac{1}{4}) = 4$ $6x-2 = 4$ $6x = 6$ $x = 1$ The solution is $\enspace x = 1, \enspace y = -\dfrac{1}{4}$.